Animate a texture / material over a mesh
Hard to give an exact answer without knowing exactly which effect you want to achieve, but...

Your object needs a UV map. Here, I've just put a seam down the edge-loop in the crease, and hit 'U' ...



.. I'm sure you could be more sophisticated about that. Maybe make use of 'Follow Active Quads' if you want the repeat in the texture to reflect the topology of the object more closely.

Optionally..



You could simplify your shader tree, a Mapping node could replace the separate nodes to animate the UV space, and you could replace the 'Add Shader' node with a 'Mix Shader' node if you want a bit more control over transparency.



Obviously, you may want different motion, scale, etc.